ORBi Collection: Mathematics
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Special issue dedicated to the 14th "Journées montoises d'informatique théorique"
http://hdl.handle.net/2268/178709
Title: Special issue dedicated to the 14th "Journées montoises d'informatique théorique"
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<br/>Editor: Bruyère, Véronique; Jungers, Raphaël; Hollanders; Rigo, Michel
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<br/>Commentary: The conference was held in Louvain-La-Neuve, September 11th - 14th, 2012Thu, 26 Feb 2015 09:52:32 GMTSpecial issue dedicated to the second "AutoMathA conference"
http://hdl.handle.net/2268/178707
Title: Special issue dedicated to the second "AutoMathA conference"
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<br/>Editor: Bruyère, Véronique; Pin, Jean-Eric; Restivo, Antonio; Rigo, Michel
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<br/>Commentary: The conference was held in Liège June 8-12, 2009.Thu, 26 Feb 2015 09:48:19 GMTDefining multiplication in some additive expansions of polynomial rings
http://hdl.handle.net/2268/178705
Title: Defining multiplication in some additive expansions of polynomial rings
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<br/>Author, co-author: Point, Françoise; Rigo, Michel; Waxweiler, Laurent
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<br/>Abstract: Adapting a result of R. Villemaire on expansions of Presburger arithmetic, we show how to define multiplication in some expansions of the additive reduct of certain Euclidean rings. In particular, this applies to polynomial rings over a finite field.Thu, 26 Feb 2015 09:27:58 GMTAnother Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words (long version)
http://hdl.handle.net/2268/178703
Title: Another Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words (long version)
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<br/>Author, co-author: Rigo, Michel; Salimov, Pavel
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<br/>Abstract: The binomial coefficient of two words $u$ and $v$ is the number of times $v$ occurs as a subsequence of $u$. Based on this classical notion, we introduce the $m$-binomial equivalence of two words refining the abelian equivalence. Two words $x$ and $y$ are $m$-binomially equivalent, if, for all words $v$ of length at most $m$, the binomial coefficients of $x$ and $v$ and respectively, $y$ and $v$ are equal. The $m$-binomial complexity of an infinite word $x$ maps an integer $n$ to the number of $m$-binomial equivalence classes of factors of length $n$
occurring in $x$. We study the first properties of $m$-binomial equivalence. We compute the $m$-binomial complexity of two classes of words: Sturmian words and (pure) morphic words that are fixed points of Parikh-constant morphisms like the Thue--Morse word, i.e., images by the morphism of all the letters have the same Parikh vector. We prove that the frequency of each symbol of an infinite recurrent word with bounded $2$-binomial complexity is rational.
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<br/>Commentary: This is an extended version of the conference version. In particular, it contains a new discussion about frequencies of symbols when the $2$-binomial complexity is bounded.Thu, 26 Feb 2015 09:23:51 GMTAvoiding 2-binomial squares and cubes
http://hdl.handle.net/2268/178702
Title: Avoiding 2-binomial squares and cubes
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<br/>Author, co-author: Rao, Michaël; Rigo, Michel; Salimov, Pavel
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<br/>Abstract: Two finite words $u,v$ are $2$-binomially equivalent if, for all words $x$ of length at most $2$, the number of occurrences of $x$ as a (scattered) subword of $u$ is equal to the number of occurrences of $x$ in $v$. This notion is a refinement of the usual abelian equivalence. A $2$-binomial square is a word $uv$ where $u$ and $v$ are $2$-binomially equivalent.
In this paper, considering pure morphic words, we prove that $2$-binomial squares (resp. cubes) are avoidable over a $3$-letter (resp. $2$-letter) alphabet. The sizes of the alphabets are optimal.Thu, 26 Feb 2015 09:18:25 GMTOn the number of abelian bordered words (with an example of automatic theorem-proving)
http://hdl.handle.net/2268/178701
Title: On the number of abelian bordered words (with an example of automatic theorem-proving)
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<br/>Author, co-author: Goc, Daniel; Rampersad, Narad; Rigo, Michel; Salimov, Pavel
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<br/>Abstract: In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in $\mathbb{Z}$ not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number of these words. In particular, over a $3$-letter alphabet, the connection with paths in the triangular lattice is made. Finally, we characterize the lengths of the abelian unbordered factors occurring in the Thue--Morse word using some kind of automatic theorem-proving provided by a logical characterization of the $k$-automatic sequences.
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<br/>Commentary: This is an extended version of the conference paper.Thu, 26 Feb 2015 09:11:14 GMTA New Approach to the 2-Regularity of the ℓ-Abelian Complexity of 2-Automatic Sequences
http://hdl.handle.net/2268/178495
Title: A New Approach to the 2-Regularity of the ℓ-Abelian Complexity of 2-Automatic Sequences
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<br/>Author, co-author: Parreau, Aline; Rigo, Michel; Rowland, Eric; Vandomme, Elise
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<br/>Abstract: We prove that a sequence satisfying a certain symmetry property is 2-regular in the sense of Allouche and Shallit, i.e., the Z-module generated by its 2-kernel is finitely generated. We apply this theorem to develop a general approach for studying the l-abelian complexity of 2-automatic sequences. In particular, we prove that the period-doubling word and the Thue--Morse word have 2-abelian complexity sequences that are 2-regular. Along the way, we also prove that the 2-block codings of these two words have 1-abelian complexity sequences that are 2-regular.Fri, 20 Feb 2015 17:44:07 GMTA Vectorial Regularization of the Keplerian Motion
http://hdl.handle.net/2268/178454
Title: A Vectorial Regularization of the Keplerian Motion
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<br/>Author, co-author: Condurache, D.; Martinusi, VladimirThu, 19 Feb 2015 10:07:51 GMTAbout the Rectilinear Keplerian Motion
http://hdl.handle.net/2268/178453
Title: About the Rectilinear Keplerian Motion
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<br/>Author, co-author: Condurache, D.; Martinusi, VladimirThu, 19 Feb 2015 10:04:49 GMTComputing the Logarithm of Homogenous Matrices in SE(3)
http://hdl.handle.net/2268/178452
Title: Computing the Logarithm of Homogenous Matrices in SE(3)
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<br/>Author, co-author: Condurache, D.; Martinusi, VladimirThu, 19 Feb 2015 10:02:58 GMTA Tensorial Explicit Solution to The Darboux Equation
http://hdl.handle.net/2268/178450
Title: A Tensorial Explicit Solution to The Darboux Equation
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<br/>Author, co-author: Condurache, D.; Martinusi, VladimirThu, 19 Feb 2015 09:53:50 GMTRemarks on the Hamiltonian of A Particle in A Rotating Reference Frame
http://hdl.handle.net/2268/178374
Title: Remarks on the Hamiltonian of A Particle in A Rotating Reference Frame
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<br/>Author, co-author: Martinusi, Vladimir; Condurache, D.Sun, 15 Feb 2015 09:03:54 GMTSpectral properties of a pseudo-integrable map: the general case
http://hdl.handle.net/2268/178316
Title: Spectral properties of a pseudo-integrable map: the general case
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<br/>Author, co-author: Bogomolny, E; Dubertrand, Rémy; Schmit, C.
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<br/>Abstract: It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In Bogomolny and Schmit (2004 Phys. Rev. Lett. 93 254102) statistical properties of a certain quantized pseudo-integrable map had been calculated analytically but only for a special sequence of matrix dimensions.
The purpose of this paper is to obtain the spectral statistics of the same quantum map for all matrix dimensions.Fri, 13 Feb 2015 14:18:55 GMTENSO forecast using a wavelet-based mode decomposition
http://hdl.handle.net/2268/178302
Title: ENSO forecast using a wavelet-based mode decomposition
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel; Fettweis, Xavier
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<br/>Abstract: We introduce a new method for forecasting major El Niño/ La Niña events based on a wavelet mode decomposition. This methodology allows us to approximate the ENSO time series with a superposition of three periodic signals corresponding to periods of about 31, 43 and 61 months respectively with time-varying amplitudes. This pseudo-periodic approximation is then extrapolated to give forecasts. While this last one only resolves the large variations in the ENSO time series, three years hindcast as retroactive prediction allows to recover most of the El Niño/ La Niña events of the last 60 years.Fri, 13 Feb 2015 12:01:07 GMTMatematica. 55 de teste pentru bacalaureat
http://hdl.handle.net/2268/178151
Title: Matematica. 55 de teste pentru bacalaureat
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<br/>Author, co-author: Pitu, Leon; Martinusi, VladimirTue, 10 Feb 2015 09:21:32 GMTA Matrix-Analytic approach to the N-player ruin problem
http://hdl.handle.net/2268/178102
Title: A Matrix-Analytic approach to the N-player ruin problem
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<br/>Author, co-author: Swan, Yvik; Bruss, F. Thomas
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<br/>Abstract: Consider N players, respectively owning x\, xi,..., x^ monetary units, who play a sequence of games, winning from and losing to each other integer amounts according to fixed rules. The sequence stops as soon as (at least) one player is ruined. We are interested in the ruin process of these N players, i.e. in the probability that a given player is ruined first, and also in the expected ruin time. This problem is called theN-player ruin
problem. In this paper, the problem is set up as a multivariate absorbing Markov chain with an absorbing state corresponding to the ruin of each player. This is then discussed
in the context of phase-type distributions where each phase is represented by a vector of
size N and the distribution has as many absorbing points as there are ruin events. We use this modified phase-type distribution to obtain an explicit solution to the N-player problem. We define a partition of the set of transient states into different levels, and on
itgive an extension of the folding algorithm (see Ye and Li (1994)). This provides an efficient computational procedure for calculating some of the key measures.Sun, 08 Feb 2015 05:32:32 GMTDes objets mentaux "aire" et "volume" au calcul des primitives
http://hdl.handle.net/2268/178094
Title: Des objets mentaux "aire" et "volume" au calcul des primitives
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<br/>Author, co-author: Gilot, MargueriteSat, 07 Feb 2015 16:38:57 GMTuelle définition du concept de tangente ? Pour quelles raisons ?
http://hdl.handle.net/2268/178081
Title: uelle définition du concept de tangente ? Pour quelles raisons ?
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<br/>Author, co-author: Balhan, Kevin; Schneider-Gilot, Marguerite; Krysinska, Marysa
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<br/>Abstract: Dans le présent article, nous présentons un parcours didactique visant à faire évoluer chez les élèves le concept de tangente, de leur connaissance antérieure de tangente à un cercle comme droite ne coupant la courbe qu’en un seul point jusqu’à une définition formalisée au sein d’un cours d’analyse. Nous montrons ainsi qu’une définition d’un objet mathématique n’est ni définitive, ni une simple description de l’objet. Le choix d’une définition au détriment d’une autre doit se faire à la lumière d’un projet plus global relatif à l’institution à laquelle elle appartient.Fri, 06 Feb 2015 17:23:15 GMTUN MILIEU CINÉMATIQUE POUR L'ÉLABORATION D'UNE PRAXÉOLOGIE « MODÉLISATION » DU THÉORÈME FONDAMENTAL DU CALCUL DIFFÉRENTIEL ET INTÉGRAL
http://hdl.handle.net/2268/178080
Title: UN MILIEU CINÉMATIQUE POUR L'ÉLABORATION D'UNE PRAXÉOLOGIE « MODÉLISATION » DU THÉORÈME FONDAMENTAL DU CALCUL DIFFÉRENTIEL ET INTÉGRAL
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<br/>Author, co-author: Balhan, Kevin
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<br/>Abstract: The text is related to the calculus’s main theorem learning as it is studied by students in the last year of Belgium secondary school. We make an epistemological analysis of the theorem that inspired us the set up of a situation composed of four mathematics statements and for which we need rectilinear movements with or without variable speeds, speeding and moving laws, areas, volumes and flows. The suggested strategies for these statements and the reactions will be analysed later.Fri, 06 Feb 2015 17:11:03 GMTUne situation fondamentale pour le concept de limite ? Questin de langage, de culture ? Comment la Théorie Anthropologique du Didactique permet-elle de problématiser cette question ?
http://hdl.handle.net/2268/177971
Title: Une situation fondamentale pour le concept de limite ? Questin de langage, de culture ? Comment la Théorie Anthropologique du Didactique permet-elle de problématiser cette question ?
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<br/>Author, co-author: Job, Pierre; Schneider-Gilot, MargueriteWed, 04 Feb 2015 15:00:38 GMT